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Abstract

Energy transfer between the interacting waves in a distributed Brillouin sensor can result in a distorted measurement of the local Brillouin gain spectrum, leading to systematic errors. It is demonstrated that this depletion effect can be precisely modelled. This has been validated by experimental tests in an excellent quantitative agreement. Strict guidelines can be enunciated from the model to make the impact of depletion negligible, for any type and any length of fiber.

Figures (12)

Fig. 1 Situation maximizing the impact of depletion (worst case situation): the pump pulse gradually transfers a fraction of its power to the continuous probe wave through the intercession of the acoustic wave created by the stimulated Brillouin scattering process. The Brillouin gain distribution is analyzed by scanning the pump-probe frequency difference and the pump pulse power is the same at the fiber input for any frequency difference, as shown in the left circle. If the Brillouin gain spectrum is uniform along most of the initial section of the fiber, the gradual power transfer between pump and probe is maximized at the peak gain frequency and non-uniform pump pulse power as a function of the frequency difference can result from this gradual depletion at the end of this uniform segment, as shown on the right circle. If a following fiber section with a slightly shifted gain spectrum is present, it is analyzed with a non-constant pump power for all frequencies and the measured gain spectrum of this section is distorted.

Fig. 2 Effect of a non-uniform frequency distribution of the pump pulse power on the measurement of the Brillouin gain spectrum: if the pump power is reduced by a fraction d at a given frequency and a Brillouin gain spectrum is analyzed with a peak gain frequency shifted by δν from this given frequency, a distorted Brillouin gain spectrum will be measured, as shown on the right (thick solid line). The measured peak gain frequency is shifted with respect to the real gain spectrum (thin solid line) and suffers from a systematic error.

Fig. 3 Left: Systematic error normalized to the FWHM Brillouin gain linewidth, as a function of the normalized frequency shift between the gains in the long initial uniform segment and the local analyzed segment, for 3 different depletion factor d. The maximum error occurs when the 2 gain spectra are shifted by a quarter of linewidth. Right: Maximum tolerable depletion as a function of the maximum tolerable normalized error, in the situation of the relative frequency shift δν leaving the maximum systematic error. The exact solution given by Eq. (8) is represented, as well as the 2nd order approximation given by Eq. (9). It shows that this approximation is excellent for depletion factors d < 0.2. Points for typical errors in standard G.652 fibers at a wavelength of 1550 nm are shown.

Fig. 4 General spectral arrangement of pump (PP) and probe signals (PisL, PisU), including most practical situations in real Brillouin distributed sensors. The arrows indicate the directions of the power transfer due to the interaction and (signal in red propagates forwardly along the fiber, those in blue backwardly). The sensors may operate in gain regime (PisU = 0), in loss regime (PisL = 0) or in double-sideband configuration (PisU = PisU).

Fig. 5 Left: Experimental layout to measure the effects of depletion and to compare them with the model. A hot spot positioned near the far fiber end showing a 10 K shift in temperature is close to the worst case situation where the depletion effect are maximized. Right: Distribution of Brillouin frequency shift along the long fiber to validate its uniformity.

Fig. 7 Left: Depletion factor d as a function of the input power of the CW signal, for a fixed input pump peak power Pip of 70 mW. Red squares are experimental points with error bars, while the solid black line is the model prediction. Right: Depletion factor d as a function of the input pump peak power of the, for a fixed input power of the CW signal Pis = 1.91 mW. Red squares are experimental points with error bars, while the solid black line is the model prediction. The pump power has no impact on the amount of depletion, while it changes the signal gain linearly (red crosses).

Fig. 8 Output pump pulse peak power as a function of the frequency difference between pump and signal in the double probe wave configuration, for 4 different values of the input power PisL of one of the signals. The 2 signals show very identical powers.

Fig. 9 Left: Depletion factor d in the double probe wave configuration as a function of the input power of the one of the CW signals, for a fixed input pump peak power Pip of 60 mW. Red squares are experimental points with error bars, the solid black line is the model prediction. Right: Depletion factor d as a function of the input pump peak power of the, for a fixed input power of one of the CW signal PisL = 2.48 mW. Red squares are experimental points with error bars, while the solid black line is the model prediction. The pump power has a slight impact on the amount of depletion, while it keeps changing the signal gain linearly (red crosses).

Fig. 10 Brillouin gain spectrum measured within the 10 m hot spot described in Fig. 5 when its temperature is shifted by 10 K, for different powers of the CW signal and for a fixed pump peak power of 69 mW. The colored curves are obtained when the hot spot is placed at the far end, while the black reference curves are for a hot spot placed at the near end. This clearly shows the skewed distortion of the gain spectrum.

Fig. 11 Brillouin frequency shift as function of the position along the hot spot, for different power Pis of the CW signal. In case A, the hot spot is placed at the far end (see Fig. 5) and the strongest biasing effect of depletion is experienced, while in case B, the hot spot is placed at the near end where the pump has not yet accumulated any depletion and the measured Brillouin frequency shift is identical for all probe powers.